What three numbers have an average of 656?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 656. This means if we add these three numbers together and divide by 3, we should get 656.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 656 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 656 * 3 = x + y + z
- So, the sum of our three numbers should be: 1968
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1968.
Solution 1:
656, 656, 656
Verification:
(656 + 656 + 656) / 3 = 1968 / 3 ≈ 656
This solution is correct!
Solution 2:
656, 656, 656
Verification:
(656 + 656 + 656) / 3 = 1968 / 3 ≈ 656
This solution is correct!
Solution 3:
1609, 257, 102
Verification:
(1609 + 257 + 102) / 3 = 1968 / 3 ≈ 656
This solution is correct!
Solution 4:
1748, 13, 207
Verification:
(1748 + 13 + 207) / 3 = 1968 / 3 ≈ 656
This solution is correct!
Solution 5:
688, 683, 597
Verification:
(688 + 683 + 597) / 3 = 1968 / 3 ≈ 656
This solution is correct!
Explanation:
As you can see, there are many possible solutions. We can find more by:
- Choosing any two numbers
- Subtracting their sum from 1968 to get the third number
Remember:
- The numbers don't have to be whole numbers.
- They can even be negative (although that might not make sense in some real-world contexts).
- The order of the numbers doesn't matter for the average.